Tuesday, September 22, 2015

Lapse Rates for Dummies or Smarties, With & Without Greenhouse Gases

Some commenters have claimed that a theoretical pure Nitrogen (N2) Earth atmosphere without any IR-active 'greenhouse gases' could not have a lapse rate nor a Maxwell et al gravito-thermal greenhouse effect.However, many prior posts have shown this to be false for a number of reasons, including two posts quoting the Feynman lectures on statistical mechanics of a Boltzmann Distribution pure N2 atmosphere, and the HS post, "Why Greenhouse Gases Don't Affect the Greenhouse Equation or Lapse Rate," which also calculates a pure N2 Boltzmann Distribution for Earth. We will now use a couple of illustrations for smarties or dummies to understand why the so-called 'greenhouse gas' water vapor cools, not warms, the Earth surface by up to ~25C via changes in heat capacity (Cp) alone (not even including additional cooling from latent heat transfer or clouds). We will also show why a pure N2 atmosphere without any greenhouse gases would have a surface temperature ~25C warmer than the present, due to a much steeper lapse rate.Recall that the dry adiabatic lapse rate formula is a very simple, linear relationship whereby the change in temperature (dT) with change in height from the surface (dh) is solely dependent upon the gravitational acceleration constant (g) divided by the heat capacity of the atmosphere at constant pressure (Cp):dT/dh = -g/CpAnd note that change in temperature dT is inversely related to change in heat capacity (Cp). Since water vapor has a much higher heat capacity Cp than air or pure N2, addition of water vapor greatly decreases the lapse rate (dT/dh) by almost one-half (from ~9.8K/km to ~5K/km), thereby cooling, not warming, the surface by up to 25C. In our hypothetical 1st atmosphere consisting only of N2 plus addition of < 1% water vapor, we assume the addition of water vapor creates a wet adiabatic lapse rate of 5K/km, the same as the wet adiabatic lapse rate on Earth. By calculating the center of mass as the HS Greenhouse Eqn does, and calculating the fixed 255K equilibrium temperature between the Earth and Sun, we can then calculate the entire tropospheric temperature profile from the surface to tropopause, and replicate the 1976 US Standard Atmosphere model:

Thought experiment 1 of a N2 atmosphere with < 1% GHG water vapor. Note for easy illustrative purposes only, the actual numbers are rounded slighly, e.g. the actual height of the center of mass is ~5.1km rather than 5.0 km, and the actual dry adiabatic lapse rate is ~9.8K/km, not 10K/km.

Note in the above "greenhouse atmosphere," there is a ~33C "greenhouse effect" from the 255K center of mass to the ~288K surface, as well as an even larger "anti-greenhouse effect" of negative 35K from the 255K center of mass to the ~220K top of troposphere. Thus, gravity has not added any energy to the atmospheric system; gravity has simply redistributed the available energy from the only source the Sun, more towards the surface and less towards the top of the troposphere. That is the gravito-thermal greenhouse effect of Poisson, Maxwell, Clausius, Carnot, Boltzmann, Feynman, US Std Atmosphere, HS greenhouse eqn et al, and has no dependence whatsoever upon IR emission/absorption from greenhouse gases.

Now lets consider a hypothetical Earth atmosphere without any greenhouse gases, consisting solely of pure N2. We again use the dry lapse rate equation above, since obviously N2 is affected by gravity (g) and has a heat capacity (Cp). In this pure N2 Boltzmann distribution, the lapse rate can thus be calculated as ~10K/km, essentially the same as our present atmosphere dry lapse rate (9.8K/km).

For illustrative purposes only, the atmospheric mass of a pure N2 atmosphere is close to that of our present atmosphere, and thus the center of mass is also located near ~5km in the troposphere. However, since the lapse rate is much steeper in a pure N2 atmosphere, the "greenhouse effect" is about 50K from the 255K center of mass to 305K surface, and the "anti-greenhouse effect" is also ~50K from the 255K center of mass to the ~205K top of the troposphere, producing a ~100K temperature gradient from the surface to top of the troposphere:

Thus, we find the net effect of the addition of < 1% 'greenhouse gas' water vapor was to cool, not warm the surface of an N2 atmosphere by up to ~25C. Thus, the Arrhenius radiative greenhouse theory (which confuses the cause with the effect) is once again demonstrated to be unphysical and falsified, and the Maxwell et al gravito-thermal greenhouse effect once again vindicated. One and only one of these two competing greenhouse theories can be correct, otherwise the observed effect would be double (66C) that observed (33C). The Maxwell et al theory is the only option which does not violate any laws of thermodynamics.

35 comments:

If the surface temperature is determined by mass and gravity at any given level of insolation then the effect of radiative gases should be zero. No warming OR cooling or, alternatively, warming beneath ascending columns equal to cooling beneath descending columns

I think one needs to consider that the thermal effects of GHGs are of opposite sign above and below the point of hydrostatic balance and within descending columns of air as compared to ascending columns of air so that at equilibrium it all nets out to zero.

If GHGs (or anything else) were to reduce decompression in the ascending column so that the surface warms then they also cause a reduction in compression in the descending column so that the surface cools by virtue of the vertical displacement of air without a change in temperature attributable to the undulations of tropopause height.

I'm planning a more detailed description of that aspect for release shortly.

I am afraid all the atmosphere would end up being almost at the same temperature.A hot parcel of air heated at the ground would raise and cool, but could be hotter than the surrounding air and raise indefinitely. It can not loose heat because it is not radiating.The only way to gain or loose heat is by contact with the ground and surrounding air.Some convection might take place from pole to equator and by day/night, but very limited as only conduction/convection transfer heat from ground.You might end up that the temp change with hight is less than the lapse rate, blocking most convection.

A column of pure N2 in a gravitational field (and of course a heat source at the bottom to inflate the N2) is obviously subject to gravity, and has a heat capacity Cp, and thus convection and a gravito-thermal GHE defined by the lapse rate

-g/Cp

Within the Boltzmann distribution. Please see the HOCKEYSCHTICK.BLOGSPOT.COM Boltzmann distribution post linked above, and the Feynman posts which also calculate a Boltzmann distribution in a pure N2 atmosphere.

My problem is that the gravito thermal hypothesis suggests that the surface temperature remains the same regardless of the radiative capability of atmospheric constituents.

In the above post you suggest that a non GHG atmosphere would produce a hotter surface.

That would be so beneath ascending columns of air because convection has to work harder if it gets no help in radiating energy to space via radiative gases. To that extent you are correct.

However, the hotter surface beneath ascending columns is then offset by a cooler surface beneath descending columns. That bit is currently missing from both AGW theory and your above post.

It is that vertical displacement at the tropopause with no change in temperature that makes the difference to the amount of compression heating that occurs within a descending column.

If the ascending column in a Nitrogen atmosphere pushes the tropopause higher due to a higher surface temperature which causes stronger convection then any vertical displacement of the tropopause (with no change in temperature) between ascending and descending columns also increases so that there is less vertical distance back to the surface in descending columns during which compression heating can occur and the surface beneath descending columns will not heat up as much as it would have done if there had been no vertical displacement at the tropopause.

I agree that I didn't go into that in full detail in my previous article which is why I have another in preparation.

"My problem is that the gravito thermal hypothesis suggests that the surface temperature remains the same regardless of the radiative capability of atmospheric constituents."

I don't see how that can be true given the large difference in lapse rates between a pure N2 atmosphere (~10 K/km) and a N2 + "wet" H2O atmosphere (~5K/km).

Both lapse rates must pivot around the center of mass, thus gravity redistributes all available solar energy over a ~100K temperature gradient in the pure N2 atmosphere, and over a ~68K temperature gradient in the N2+H2O atmosphere, but the so-called average kinetic temperature in both atmospheres remains the exact same as the 255K equilibrium temperature with the Sun. No 1st or 2nd law violations whatsoever.

The ground would be -5C dependent on the albedo of the ground. (assuming no clouds)The N2 atmosphere would only redistibute some heat between equator and the poles.How much that could be is limited by the airs convective heating and coolig from contact with the ground. The heat conduction in N2 is very limited.

I'm sorry, I don't agree at all that a pure N2 column would be isothermal, neither does Feynman, nor Maxwell, Poisson, US Std Atmosphere (which completely removed all CO2 from their model), Carnot, Helmholtz, Clausius, Boltzmann, etc etc.

I've repeatedly posted all of the mathematics proving this is true for each of these giants of physics. Saying a bunch of words without any mathematical support (as I have provided in dozens of posts) is quite unconvincing.

Please explain how the ground could be more than -5C when the atmosphere is invisible for the radiation.Any higher temperature than the -5C would radiate more power out than received by the Sun. The atmosphere only helps to redistribute some of the heat to the less insolated areas.

All that gravity does is redistribute the kinetic heat energy from the Sun, more kinetic energy (KE) and less gravitatitional potential energy (PE) toward the surface, and vice-versa toward the top of the troposphere. There is no added energy to the system from gravity, just a linear re-distribution in the troposphere, i.e. the lapse rate -g/Cp.

In both the non-GHG & GHG atmospheres, the surface temperature is thus "enhanced" and the top of troposphere temperature is "diminished" in comparison to the equilibrium temperature with the Sun, 255K. In both atmospheres, the "average" statistical distribution of temperature is 255K, and Ein = Eout by the 1st law.

The problem with your model is you assume solar radiative input to be in equilibrium with the 255K Temp at the middle of the atmosphere. However if the atmosphere does not absorb or emit IR radiation there can be no principled reason to assume this. Radiatively the Nitrogen atmosphere is irrelevant. The only emitter/radiator in the system is the ground. Yet the equilibrium with the sun and background 3K space must be radiatively achieved. The transparent atmosphere might as well not be there. This is trivially obvious point.

"The problem with your model is you assume solar radiative input to be in equilibrium with the 255K Temp at the middle of the atmosphere."

Not a problem at all, in fact the HS greenhouse equation PERFECTLY reproduces the 1976 Standard Atmosphere, and calculates both the surface temperature and temperature profile of the troposphere.

It is true, as I've stated hundreds of times on this blog, that a pure N2 atmosphere only emits from the surface, but this does NOT negate the thermal enhancement of the surface from mass/gravity/pressure, on Earth or the 7 other planets for which we have adequate data.

Explain how Jupiter (composed almost entirely of H2 & He) emits 67% more energy than it receives from the Sun, how the top of Uranus atmosphere can have storms hotter than require to melt steel, how Venus temperature is easily explained by the Ideal Gas Law alone, etc etc:

If you by "commenters" refer to me you have obviously not understood my comments. I never claimed that a "pure Nitrogen (N2) Earth atmosphere without any IR-active 'greenhouse gases' could not have a lapse rate". Of course a pure N2-atmosphere will have a lapse rate since it is heated from the surface and cools at higher altitudes because kinetic energy (heat) converts to potential energy (not heat) upon ascent.

What I previously said was that the Effective Radiative Level (ERL) had to be at the surface of a planet with an non-radiative pure N2 atmosphere, and you agreed. Note that ERL is not the same as the centre of mass (CoM) for the atmosphere in this case, which seems to be critical for your theory. Only with radiatively active gases in the atmosphere could ERL equal CoM.

I will rephrase my question from before and it relates to several comments by Svend where I also think you have not replied on the specific issue raised.

How can a planet, that is identical to earth but with an atmosphere of pure N2 and with a surface temperature of 305 K (from your calculation above), radiate the same amount of energy into space as an identical but atmosphere-less planet at 255 K?

The radiative properties of these planets should be exactly the same since N2 is radiatively inactive at these temperatures. For both these planets the surface would have to be 255 K to be in radiative equilibrium with the sun and space. The distribution of heat or gases in the atmosphere is irrelevant and so is convection. Only the surface can radiate energy and there is nothing in the atmosphere to slow down the emission of radiation, which of course would have increased the temperature if energy input from the sun is constant.

You would have to claim that an N2 atmosphere changes the radiative properties of the surface and consequently also Stefan-Bolzmann's law, or that this law does not apply to planets with atmospheres. I think this is physically questionable and it is not something you are claiming in these posts anyhow.

This example shows that either your theory is dependent on greenhouse gases to make the ERL equal to CoM, or that it is simply wrong.

In the pure N2 atmosphere the surface temperature enhancement from gravity/mass/pressure is 305-255 = 50K gravito-thermal GHE, equal and opposite to the -50K anti-greenhouse effect from the center of mass at 255K to the top of the troposphere at 205K. Gravity/pressure just redistributes the kinetic energy more toward the surface and less toward the top of the troposphere, the "average" kinetic temperature of the entire atmosphere is the equilibrium temperature of 255K.

"You would have to claim that an N2 atmosphere changes the radiative properties of the surface and consequently also Stefan-Bolzmann's law, or that this law does not apply to planets with atmospheres."

An N2 atmosphere DOES change the radiative properties of the surface by exchanging conductive energy with the surface and moving it up and down in convection.

The S-B law does apply to planets with atmosphere BUT ONLY when the planet is observed from an external vacuum. That law says nothing about what the surface temperature would be beneath an atmosphere.

MS,it doesn't matter what the average temperature of the atmosphere is, it is only the surface temperature that determines the emission of radiation from a planet with a non-radiative atmosphere. Only with greenhouse gases present would it be meaningful to discuss the average temperature of the entire atmosphere in relation to emission of radiation.

You are again just repeating your other argument, which does not address the issue I have raised, and Svend as well. Could you please answer how a surface at 305K can radiate the same amount of energy into space as if it was at 255K? (without invoking greenhouse gases of course)

Stephen,what do you mean by "...exchanging conductive energy"? Do you mean that the interaction of the N2 atmosphere with the surface removes heat from the surface by conduction? Sure, this could happen, but then the average surface temperature will be lower than the 305K that MS predicted, so disproving the theory. In fact for your argument to make sense the temperature of the surface would have to be lowered to 255K, otherwise the same radiative issue would still apply. Are you agreeing with this? This still disproves the gravitothermal theory.

I understand that local temperatures at the surface can be higher or lower but we are talking about the average surface temperature that determines the average emission of radiation from the planet.

Good that we agree that Stefan-Bolzmann's law is valid for our discussions! Although, for a radiatively inactive atmosphere it doesn't matter if you observe the planet from the vacuum in space or from within the atmosphere. If the atmosphere does not interact with the radiation this point is irrelevant. But sure, when observing a system that contain greenhouse gases of course we should observe it from the vacuum in space. Makes no difference for my argument however.

If the radiation does not interact with the atmosphere on it's way out of course we can say something about the surface temperature. I repeat, it is only the surface that can emit or absorb radiation in this system so the emission from the planet, observed from an external vacuum, will be proportional to [surface temperature]^4 in accordance with Stefan-Boltzmann's law. At radiative equilibrium this would mean T=255K with or without an atmosphere of pure N2.

Indeed it is the same amount of radiation that is observed from space for earth that also contain greenhouse gases. But here we can measure the surface temperature and it is on average 288K. So I agree that just measuring the total radiation from a planet will not tell us directly what the surface temperature will be, but if we can not detect any radiatively active gases in the atmosphere we can for sure say that all emitted radiation must come unperturbed from the surface. Otherwise you would have to come up with a theory of how the atmosphere can interact with the radiation without interacting with it. And your argument of convection does not work as I explained above, if I understood it correctly.

The surface is at 305K and radiates at 305K to space, from the surface in a pure N2 atmosphere. How is this possible? Gravity "steals" the kinetic heat energy from the center of mass to top of the troposphere (a negative 50K anti-greenhouse effect) and redistributes that kinetic energy toward the surface thus enhancing the surface temperature 50K above the equilibrium temperature of 255K.

You are forgetting that this is a dynamic system and that the irradiance calculated with Stefan-Boltzmann's equation is in W/m^2, i.e. J/s per sq meter, so a rate. This means that for a surface at 305K, every second there is a certain amount of extra heat leaving it compared to what arrives from the sun.

For your theory to work you would have to redistribute or "steal" the excess energy from the top to the surface every second. So the top of the troposphere would have to get colder and colder to provide the energy for the surface to continuously irradiate at temperatures higher than 255K, eg. 305K or 288K.

Maybe you would claim that there is some additional energy source to reheat the top troposphere? Note however that you can not use any of the solar energy to compensate because then you have to subtract that from the energy that would have heated the surface instead. In a pure N2-atmosphere there is anyhow no way for solar energy to be absorbed anywhere in the atmosphere.

Remember also you have claimed that the gravitothermal effect do not produce any new heat but only redistributes the already present heat. This can however not be the case in a dynamic system as noted above since the top atmosphere would have to get colder and colder.

Martin, please read the Feynman posts (which also quote Maxwell extensively). Feynman shows why a pure N2 atmosphere or O2/N2 atmosphere would establish a Boltzmann distribution tropospheric temperature gradient purely on the basis of statistical mechanics in a gravity field. He does so without one single greenhouse gas or radiative calculation whatsoever.

The top of the troposphere does not have to get colder & colder, just to ~205K, is 50K less than the 255K equilibrium temperature, which is exactly equal and opposite to the 50K surface temperature enhancement. The pure N2 atmosphere atmosphere has convection and conduction which is constantly fighting against gravity, converting KE to PE back and forth. THAT is the gravito-thermal temperature gradient or very-poorly named "GHE".

Sorry MS, I'm afraid you are wrong. Feynman is not showing that gravity establishes a temperature gradient on its own. He is assuming a constant temperature throughout the atmosphere at any altitude, which completely contradicts your theory. I will give you four quotes from your excerpts from Feynman's book that you posted on 29th of July.

First sentence(!): "If the temperature is the same at all heights, the problem is to discover by what law the atmosphere becomes tenuous as we go up."

At the end of the second sentence: "... if we know the number of molecules per unit volume, we know the pressure, and vice versa: they are proportional to each other, since the temperature is constant in this problem."

In the sentence just before eq. 40.1: "Since P=nkT, and T is constant, we can eliminate either P or n, say P, and get dn/dh=-(mg/kT)n"

Note, here it is clear that temperature is constant and independent of the altitude difference dh.

Towards the end of the first section where you even highlighted the sentences:"This does not really happen in our own atmosphere, at least at reasonable heights, because there is so much agitation which mixes the gases back together again. It is not an isothermal atmosphere. "

I can understand that you somehow think the last sentence would apply to the theory he presents but it is clear from the first three quotes that he assumes a constant temperature throughout the atmosphere. So he must mean that the theory he presents can not be directly applied to earths atmosphere without taking other things into account, such as the preferential heating of earths surface by solar energy.

Furthermore, nowhere in the excerpts you present is there any temperature differential (dT). Obviously because Feynman assumes constant temperature throughout the atmosphere at any altitude.

So unfortunately it is pretty clear that you have misinterpreted Feynman and should stop referring to him in support for your theory.

You wrote above: "...convection and conduction which is constantly fighting against gravity, converting KE to PE back and forth."

The energy for the convection and the KE that converts to PE comes completely from solar energy that has heated the surface, so you have to subtract that energy from the amount that heats the surface. The temperature of the surface would become lower by this process. Since gravity is a conservative force field the KE released from stored PE is the same amount that initially arrived in the form of solar energy so there is no net heating of the surface or atmosphere that could explain why the surface is at 288K and not 255k.

I also repeat my previous question. You have so far avoided to answer it.So, how can a surface at 305K, below a non-radiative atmosphere, radiate as if it was only at 255K? This is independent of the distribution of heat or gases in the atmosphere.

Sorry Martin, it is you who is wrong. Feynman works through a thought experiment, beginning with the assumption the column would be isothermal, and then shows why statistical mechanics of a Boltzmann Distribution prove that is not the case for a PURE N2 atmosphere column in a gravity field, and obviously with a heat source at the bottom to inflate the N2 (otherwise the N2 would atmosphere would collapse to the surface and freeze).

I'm sorry, but I don't have time to continue to tutor you personally any further, so please study the hundreds of posts I've linked to on these matters and which answer your questions over and over again.

Read especially the post and links on the Volokin paper, which proves beyond any reasonable doubt (now for 8 planets) that surface temperature is only dependent upon pressure & solar insolation.

MS,I think we have different opinions on who has tutored who, but never mind. It is clear you have no answer to how a surface at 305 or 288 K can radiate into space at the same rate as if it was only 255K. I am not surprised, because the only way for this to be possible is if you have something in the atmosphere that can interact with the radiation and slow down the rate (flux) so it becomes equivalent to that of a 255K planet. And the only way to do this is to introduce radiatively active gases, i.e. greenhouse gases.

Nothing in the texts by Feynman or Maxwell, that I have seen on this blog at least, discusses this. I also note that the Volokin paper has been temporarily withdrawn by Elsevier and from what I read on the web the author is very critical to your interpretation of it. It is anyhow just another modeling paper and, if we are to believe AGW skeptics, modeling is not very reliable evidence in climate science.

I am more interested in real physical evidence. In this respect it is interesting that, even though you claim to disprove Arrhenius radiative theory in your post above, you have previously presented experimental evidence for it, here on this very blog.(!)

In your post on Wood's experiment (June 29th, 2010) it is clear that a box with an infrared (IR) active glass lid, heated by sun light, becomes almost 1 degree warmer than a box with an IR-inactive NaCl lid. Although, quantitatively, the experimental setup is very crude so drawing conclusions on the atmospheric greenhouse effect is of course difficult. But qualitatively it shows that the radiative theory is correct. You can not explain this difference by either gravity or convection but with Arrhenius radiative theory you can.

Your theory is hence not consistent with either theory or experiments. I can understand that it is difficult to admit to this since you have spent a lot of time and effort in writing a lot of posts about your theory on this blog. But how can you expect anyone else, like scientists in IPCC etc, to admit mistakes if you are not able to do that yourself? I guess the problem is that the discussion has become so polarized, by people from both sides, that admitting to any mistake becomes impossible. That's why it is important to keep a respectful tone in all discussions, which is of course difficult when you are passionate about a topic. But it is also important to be able to handle critique and keep the discussion open to different views. So I thank you for posting my comments even though I am very critical to your theory.

this is the exact same thing that Feynman does, calculate a Bolzmann distribution, also linked at the top of this post.

Volokin does produce a model using regression analysis.

I produced a model from first principles (the HS greenhouse equation) using only the 1st law, ideal gas law, Poisson relation to perfectly reproduce the US Std Atmosphere, which is the only atmospheric model verified with millions of observations. Apparently you think this is some grand coincidence. So be it, I'm not going to argue with you further.

Wood's experiment does disprove the Arrhenius GH theory.

Apparently, you also don't accept the overwhelming evidence that the gravito-thermal GHE is correct, on all 8 planets for which we have adequate data, including Venus:

Simple proof:

Assuming an atmospheric pressure of 92000 mb, a density of 67 kg/m^3 and a mean molecular mass of 43.45 (see NASA’s ‘Fact Sheet Venus’) we get a temperature of T = PV/nR = 92000/(67000/43.45*0.082) = 727K for Venus when the actual surface temperature according to NASA is 737K. Note also, only 10% of solar insolation penetrates the opaque cloud layer at the top of the Venusian atmosphere.

If that isn't proof enough for you that mass/gravity control surface temperature, I can't imagine what is.

Non radiative gases do interact with radiation flowing through by accepting conduction from the surface and convecting upwards then downwards.

One cannot assert that since convective ascent equals convective descent then the thermal effect on the surface is zero.

There is energy engaged in both raising air in the uplift column and lowering air in the descent column. One must add the two blocks of energy to arrive at the total energy involved in convective overturning.

Those two blocks of energy combined require an 'extra' energy store at the surface to maintain them and that is the gravito thermal greenhouse effect.

That energy cannot be seen from space because the Earth emits at 255k despite the surface being at 288K.

Stephen,You wrote that "the Earth emits at 255K despite the surface being at 288K".

You have to realize the massive contradiction in this. The conduction you describe has nothing to do with the black body radiation from the surface. If the surface is at 288K it has to emit at that temperature. This is independent of the convection of gases above the surface. You can not get around it.

If you are saying that the 288K of heat is somehow trapped in the atmosphere just above the 255 K surface you would have to explain how heat can be transferred from the colder surface to the then hotter lower atmosphere, which violates the second law of thermodynamics. Everyone knows that heat transfers from hot to cold and that on earth heat is transferred from the surface to the atmosphere. These two facts contradicts and hence disproves your theory.

The starting point equation should be rewritten thusly:C dT = -g dhto show that we are talking here about the thermal energy (C dT) of the slice of the atmosphere (of thickness dh) counteracting the gravitational pull exerted upon it. That's how it ends up staying in its slot within the atmosphere and not moving up or down. Even better would be to start from pV/T = const, the ideal gas law, and analyze the pressures exerted upon the slice. The buoyancy force here would balance the weight of the slice. It all comes back to the equation above. The sun enters this as a boundary condition at one end. Because this is a first order DE, you can only apply the condition at one end, then the other gets computed as you step.This works only for a static atmosphere, while the Earth atmosphere is obviously not static, especially, not the troposphere: there's a lot of movement in all three directions, and mixing here. The stratosphere, on the other hand, is very static, hence the name. But as a first approximation for the troposphere, it works quite well. More detailed considerations yield more complex equations as is discussed, e.g., by Chilingar et al in [1].The first question is why it works, the second where is radiative transfer in all this. It works because the earth atmosphere is thin enough to be approximated quite well by the ideal gas laws. As to the radiative transfer... it's incorporated in the specific heat parameter, C (it's phenomenological and has to be measured). In more elaborate computations, it is also included in heat conductivity, which is why the early NASA model of the earth's atmosphere worked so well. I've been wondering if CMIP[35] models do not end up overcomputing the radiative effect by doing it twice, once explicitly and the second time through the use of the specific heats and heat conduction coefficients.[1] doi:10.4236/acs.2014.45072

The values of specific heats can be derived from principles of microscopic physics, in particular, quantum mechanics of molecules concerned is involved, which includes rotational and vibrational states and their energy absorption properties. The energy in this case is, of course, in the form of photons and direct scattering of molecules on one another, which is electromagnetic interaction too. It's one of the goals of advanced statistical physics to get the numbers right--it's also very difficult, one of the hardest areas of theoretical physics. The heat conduction coefficient is another quantity that can be evaluated in the same way. They both show as specific terms in a certain expansion.Commenting some more on my previous comment, namely, why it works. It's not only because the ideal gas approximation is OK in this case, but also because the dynamics of the troposphere moves air masses in such a way that, on average, we end up with the kind of the static distribution you get from this model. The atmosphere equilibrates, even if not exactly at any given time, but on average it does.

I agree with Gerlich and Tscheuschner, also with Chilingar et al. and with Kramm, Dlugi and Zelger. "Greenhouse effect" is unphysical baloney. Many in the climate science community agree with this as well, conceding at the very least that the term "greenhouse effect" is a misnomer because this is not how greenhouses work. Convection matters. In greenhouses as well as in the atmosphere.